An iterative algorithm for solving the multidimensional neutron diffusion nodal method equations on parallel computers
- Oak Ridge National Lab., Oak Ridge, TN (US)
In this paper the one-group, steady-state neutron diffusion equation in two-dimensional Cartesian geometry is solved using the nodal integral method. The discrete variable equations comprise loosely coupled sets of equations representing the nodal balance of neutrons, as well as neutron current continuity along rows or columns of computational cells. An iterative algorithm that is more suitable for solving large problems concurrently is derived based on the decomposition of the spatial domain and is accelerated using successive overrelaxation. This algorithm is very well suited for parallel computers, especially since the spatial domain decomposition occurs naturally, so that the number of iterations required for convergence does not depend on the number of processors participating in the calculation. Implementation of the authors' algorithm on the Intel iPSC/2 hypercube and Sequent Balance 8000 parallel computer is presented, and measured speedup and efficiency for test problems are reported. The results suggest that the efficiency of the hypercube quickly deteriorates when many processors are used, while the Sequent Balance retains very high efficiency for a comparable number of participating processors. This leads to the conjecture that message-passing parallel computers are not as well suited for this algorithm as shared-memory machines.
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 5204366
- Journal Information:
- Nuclear Science and Engineering; (United States), Vol. 111:1; ISSN 0029-5639
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
NEUTRON DIFFUSION EQUATION
ALGORITHMS
CARTESIAN COORDINATES
COMPUTERS
EFFICIENCY
INTEGRALS
ITERATIVE METHODS
MANY-DIMENSIONAL CALCULATIONS
PARALLEL PROCESSING
TESTING
TWO-DIMENSIONAL CALCULATIONS
COORDINATES
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
PROGRAMMING
663610* - Neutron Physics- (1992-)
990200 - Mathematics & Computers